The nation's largest public pension fund—and a long-time Apple Inc. investor—isn't impressed with Carl Icahn's plans for the company.

Anne Simpson, head of corporate governance at the California Public Employees' Retirement System, blasted Icahn's demands for a larger share buyback program, demands he is considering taking to the company's shareholders.

"We are uncomfortable with a raider coming into a company with a proposal to disgorge cash," Simpson told Bloomberg News. "Carl Icahn is a Johnny come lately."

Simpson said that CalPERS, which owns about half as many Apple shares as Icahn, supports Apple's currently plans to return $100 billions to shareholders via dividends and a $60 billion buyback program.

"We like what they're doing," Simpson said. "They have a significant program for returning money to shareholders."

"Carl Icahn is late to the party. This debate's already been had. I'm not sure what Carl Icahn's proposal adds."

Icahn said he was "quite confused" by Simpson's criticism.

"I don't understand what this had to do with the democracy of voting," Icahn said. "I guess if your family didn't come over on the Mayflower, then you don't have a right to vote."

Simpson also criticized Icahn's use of Twitter to discuss his discussions with Apple CEO Tim Cook, which have sometimes taken place over a meal.

"Sending Tweets from under the dinner table—this is unseemly," she said.